Related papers: A low-rank approach to the solution of weak constr…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

This paper introduces a novel computational approach termed the Reduced Augmentation Implicit Low-rank (RAIL) method by investigating two predominant research directions in low-rank solutions to time-dependent partial differential equations…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are…

Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional…

Subspace clustering refers to the problem of segmenting a set of data points approximately drawn from a union of multiple linear subspaces. Aiming at the subspace clustering problem, various subspace clustering algorithms have been proposed…

Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…

Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points poses a major challenge. This work provides new theoretical…

This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…

Label Distribution Learning (LDL) is a novel machine learning paradigm that assigns label distribution to each instance. Many LDL methods proposed to leverage label correlation in the learning process to solve the exponential-sized output…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

Parameter-dependent discretizations of linear fluid-structure interaction problems can be approached with low-rank methods. When discretizing with respect to a set of parameters, the resulting equations can be translated to a matrix…

Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…

Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…

In recent years, large language models (LLMs) have driven advances in natural language processing. Still, their growing scale has increased the computational burden, necessitating a balance between efficiency and performance. Low-rank…

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of…

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…